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     Checking with Example 1 will show a consistent result for the triangle's Area using the conventional formula as we would expect.  Successful completion of our third example ought to have boosted our confidence and morale to the point where we are adequately prepared to conquer the highly heralded Pythagorean Theorem?
* * * 
 PYTHAGOREAN THEOREM *
     Given a right triangle, with legs (the two shorter sides) of length "a & b" and whose hypotenuse (the
Right Triangle diagram
longest side, opposite the right angle) being of length "c," then the relationship between the three sides is expressed by the Pythagorean Theorem:
a² + b²  =  c²
     Seems as good a time as any to give this concept a whirl.  Example 4 does just that (press onward)...
 

  • Example 4
    Find the length of the unknown side for the triangle shown in the illustration.
    Example 4: right triangle diagram
         The length of the bottom side is not known, so let's label it as the unknown "b" (i.e., the base of the triangle) and utilize the Pythagorean Theorem where a =  623cm (length of the other leg) & c = 923cm (length of the hypotenuse) as follows: 
    ( 923in ) ²  +  b ²   =   ( 623in ) ²  
    4449in²  +  b ²   =     9349in²  
      b ²   =     9349in²  -   4449in²
      b ²   =     49 in²
      b   =   √49      in²
      b   =    7 in  
         Once one grasps all that happened here consider
    • * The importance of this mathematical formula is difficult to overemphasize as it will be a necessity for a significant number
    of problems throughout the remainder of the course/text.
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